The present invention relates generally to wireless communications and, more particularly, to a method for generating a codebook for multiple input multiple output MIMO wireless systems.
We consider a MIMO system with m transmit antennas at the base station and a user each with n receive antennas. The complex baseband signal model is given byy=Hx+w,  (1)where x is the m×1 transmitted signal vector, H is the n×m channel matrix, w˜(0, I) is a circularly symmetric complex additive white Gaussian noise vector, and y is the n×1 received signal vector. We consider a block fading channel model in which the channel remains constant during the transmission of each packet (or codeword of length T) and it changes independently from one block to another, where the distribution of the channel state is known a priori. The average power constraint is given by E[xHx]≦P.
We consider maximizing the throughput in single user (SU-) MIMO systems (or sum-rate throughput for multiple user (MU-) MIMO systems) which is usually the primary goal in downlink transmissions. We make the following assumptions: (1) the user feeds back the quantized channel state via a limited feedback link; (2) based on the feedback information, the base station performs a linear precoding (and only linear precoding is allowed) of the transmitted streams.
Let UDV* be the singular value decomposition (SVD) of the channel matrix H. With B bits of feedback, the user quantizes the first k column of V (where k≦min(n, m) is a fixed number predetermined by the base station) using a quantization codebook Q={Q1, Q2, . . . , Q2B}, QiεCm×n, as follows
                                          V            ⋒                    ⁡                      (                          1              ⁢                              :                            ⁢              k                        )                          =                  arg          ⁢                                          ⁢                      arg                          Q              ∈              Q                                ⁢                                          ⁢                      ⅆ                          (                                                V                  ⁡                                      (                                          1                      ⁢                                              :                                            ⁢                      k                                        )                                                  ,                Q                            )                                                          (        2        )            where d(.,.) is some distance metric. The codebook design problem and the appropriate choice of the distance metric have been considered in prior art. The columns of the quantized precoding matrix {circumflex over (V)}(1:k) correspond to possible different streams for this user.
The transmitted signal x from the base station then consists of L data streams, u1, u2, . . . uL, sent through column vectors g1, g2, . . . gL of a linear precoder G. We have
                    x        =                  Gu          =                                    ∑                              i                =                1                                      ⁢                                                  ⁢                                          u                i                            ⁢                              g                i                                                                        (        3        )            In SU-MIMO systems, we have L=k while in MU-MIMO systems we have L≧k, where one or more than one stream may be intended for each user.
Conventionally, the quantized precoding codebook design for a m×n MIMO system deals with a packing of the n dimensional subspaces of an m dimensional vector space over the grassmanian manifold G(m, n). Different performance measures for such a design has been derived based on different distance metric over grassmanian manifolds. As a result, the element of each codebook entry is generally an arbitrary complex number.
Accordingly, there is a need for a method for codebook design that utilizes vector codebooks to generate the corresponding matrix codebooks for different transmission ranks, allow efficient precoder selection and the codebooks can be optimized for different scenarios (propagation environments/antenna configurations), In addition, the vector codebooks can also be designed to obtain a single codebook offering a robust performance across different scenarios.